Convection in Porous Media (eBook)

Preface to the Fourth EditionPreface to the Third EditionPreface to the Second EditionPreface to the First Edition Nomenclature   1  Mechanics of Fluid Flow through a Porous Medium1.1  Introduction               1.2  Porosity       1.3  Seepage Velocity and the Equation of Continuity      1.4  Momentum Equation:  Darcy's Law  1.4.1  Darcy's Law:  Permeability                1.4.2  Deterministic Models Leading to Darcy's Law           1.4.3  Statistical Models Leading to Darcy's Law   1.5  Extensions of Darcy's Law    1.5.1  Acceleration and Other Inertial Effects       1.5.2  Quadratic Drag:  Forchheimer's Equation   1.5.3  Brinkman's Equation           1.5.4  Non-Newtonian Fluid1.6  Hydrodynamic Boundary Conditions               1.7  Effects of Porosity Variation                1.8  Turbulence in Porous Media               1.9 Fractured Media, Deformable Media, and Complex Porous Media1.10 Bidisperse Porous Media     2  Heat Transfer through a Porous Medium2.1  Energy Equation:  Simple Case           2.2  Energy Equation:  Extensions to More Complex  Situations   2.2.1  Overall Thermal Conductivity of a Porous Medium                2.2.2  Effects of Pressure Changes, and Viscous Dissipation,2.2.3 Absence of Local  Thermal Equilibrium         2.2.4  Thermal Dispersion2.2.5 Cellular Porous Media         2.3  Oberbeck-Boussinesq Approximation            2.4  Thermal Boundary Conditions            2.5  Hele-Shaw Analogy 2.6  Bioheat  Transfer and Other Approaches      3  Mass Transfer in a Porous Medium: Multicomponent and Multiphase Flows3.1  Multicomponent Flow:  Basic Concepts          3.2  Mass Conservation in a Mixture        3.3  Combined Heat and Mass Transfer  3.4  Effects of a Chemical Reaction           3.5  Multiphase Flow      3.5.1  Conservation of Mass        3.5.2  Conservation of Momentum          3.5.3  Conservation of Energy     3.5.4  Summary:  Relative Permeabilities3.6  Unsaturated Porous Media3.7  Electordiffusion  through Porous media3.8  Nanofluids                                4 Forced Convection4.1   Plane Wall with Prescribed Temperature     4.2   Plane Wall with Prescribed Heat Flux             4.3   Sphere and Cylinder:  Boundary Layers         4.4   Point Source and Line Source:  Thermal Wakes          4.5   Confined Flow          4.6   Transient Effects     4.6.1  Scale Analysis         4.6.2  Wall with Constant Temperature  4.6.3  Wall with Constant Heat Flux          4.6.4  Other Configurations          4.7   Effects of Inertia and Thermal Dispersion:  External Flow     4.8   Effects of Boundary Friction and Porosity Variation:  External Flow4.9   Effects of Boundary Friction, Inertia, Porosity Variation, Viscous Dissipation, and Thermal Dispersion:  Confined  Flow4.10 Local Thermal Nonequilibrium4.11 Partly Porous Configurations4.12 Transversely Heterogeneous Channels and Pipes4.13 Thermal Development         4.14  Surfaces Covered with Porous Layers           4.15  Designed Porous Media     4.16  Other Configurations or Effects4.16.1  Effect of Temperature-dependent Viscosity         4.16.2  Oscillatory Flows, Counterflows  4.16.3  Non-Newtonian Fluids4.16.4  Bidisperse Porous Media4.16.5  Other Flows, Other Effects4.17  Heatlines for Visualizing Convection              4.18 Constructal Tree Networks: Flow Access in Volume-to-Point Structures        4.18.1  The Fundamental Volume-to-Point Flow Problem              4.18.2  The Elemental Volume    4.18.3  The First Construct            4.18.4  Higher-Order Constructs                4.18.5 The Constructal Law of Design and Evolution in Nature4.19 Constructal Multiscale Flow Structures; Vascular Design:     4.20  Optimal Spacings for Plates Separated by Porous Structures5.  External Natural Convection5.1  Vertical Plate             5.1.1  Power Law Wall Temperature: Similarity Solution  5.1.2  Vertical Plate with Lateral Mass Flux            5.1.3  Transient Case:  Integral Method  5.1.4  Effects of Ambient Thermal Stratification  5.1.5  Conjugate Boundary Layers             5.1.6  Higher-Order Boundary Layer Theory         5.1.7 Effects of Boundary Friction, Inertia, and Thermal Dispersion            5.1.7.1  Boundary Friction Effects5.1.7.2  Inertial Effects   5.1.7.3  Thermal Dispersion Effects           5.1.8  Experimental Investigations            5.1.9  Further Extensions of the Theory5.1.9.1  Particular Analytical Solutions5.1.9.2  Non-Newtonian Fluids5.1.9.3  Local Thermal NonEquilibrium5.1.9.4  Volumetric Heating due to Viscous Dissipation, Radiation or Otherwise5.1.9.5 Anisotropy and Heterogeneity5.1.9.6 Wavy Surface5.1.9.7 Time-dependent Gravity or Time-dependent Heating5.1.9.8 Newtonian Thermal Boundary Condition5.1.9.9 Other aspects5.2  Horizontal Plate        5.3  Inclined Plate             5.4  Vortex Instability     5.5  Horizontal Cylinder  5.5.1  Flow at High Rayleigh Number        5.5.2  Flow at Low and Intermediate Rayleigh  Number   5.6  Sphere         5.6.1  Flow at High Rayleigh Number        5.6.2  Flow at Low Rayleigh Number        5.6.3  Flow at Intermediate Rayleigh Number      5.7  Vertical Cylinder       5.8  Cone             5.9  General Two-Dimensional or Axisymmetric Surface 5.10  Horizontal Line Heat Source              5.10.1  Flow at High Rayleigh Number     5.10.1.1  Darcy Model     5.10.1.2  Forchheimer Model      5.10.2  Flow at Low Rayleigh Number      5.11  Point Heat Source 5.11.1  Flow at High Rayleigh Number     5.11.2  Flow at Low Rayleigh Number      5.11.3  Flow at Intermediate Rayleigh Number   5.12  Other Configurations           5.12.1  Fins Projecting from a Heated Base           5.12.2  Flows in Regions Bounded by Two Planes               5.12.3  Other Situations 5.13  Surfaces Covered with Hair               6  Internal Natural Convection: Heating from Below6.1  Horton-Rogers-Lapwood Problem   6.2  Linear Stability Analysis         6.3  Weak Nonlinear Theory:  Energy and Heat Transfer Results  6.4  Weak Nonlinear Theory:  Further Results      6.5  Effects of Solid-Fluid Heat Transfer: Local Thermal Non-equilibrium  6.6  Non-Darcy, Dispersion, and Viscous Dissipation Effects          6.7  Non-Boussinesq Effects        6.8  Finite-Amplitude Convection:  Numerical  Computation and Higher-Order Transitions             6.9  Experimental Observations 6.9.1  Observations of Flow Patterns and Heat Transfer  6.9.2  Correlations of the Heat Transfer Data       6.9.3  Further Experimental Observations             6.10  Effects of Net Mass Flow6.10.1  Horizontal Throughflow6.10.2 Vertical Throughflow                         6.11  Effects of Nonlinear Basic Temperature Profiles      6.11.1  General Theory  6.11.2  Internal Heating6.11.3  Time-Dependent Heating6.11.4  Penetrative Convection,  Icy Water           6.12  Effects of Anisotropy           6.13  Effects of Heterogeneity    6.13.1  General Considerations  6.13.2  Layered Porous Medium                6.13.3  Analogy between Layering and Anisotropy            6.13.4  Heterogeneity in the Horizontal Direction               6.14  Effects of Nonuniform Heating        6.15  Rectangular Box or Channel              6.15.1 Linear Stability Analysis, Bifurcation Theory, and  Numerical Studies            6.15.2  Thin Box or Slot   6.15.3  Additional Effects              6.16  Cylinder     6.16.1  Vertical Cylinder or Annulus          6.16.2  Horizontal Cylinder or Annulus     6.17  Internal Heating in Other Geometries          6.18  Localized Heating and Wavy Surface             6.19  Superposed Fluid and Porous Layers            6.19.1  Onset of Convection        6.19.1.1  Formulation      6.19.1.2  Results                6.19.2  Flow Patterns and Heat Transfer  6.19.3  Other Configurations and Effects                6.20  Layer Saturated with Water Near 4˚C           6.21  Effects of a Magnetic Field                6.22  Effects of Rotation                6.23  Other Types of Fluids or Situations6.24  Effects of Vertical Vibration and Variable Gravity6.25  Bioconvection6.26 Constructal Theory of Bénard Convection6.26.1 The Many Counterflows Regime6.26.2 The Few Plumes Regime6.26.3 The Intersection of Asymptotes 7 Internal Natural Convection: Heating from the Side7.1  Darcy Flow between Isothermal Side Walls  7.1.1  Heat Transfer Regimes      7.1.2  Boundary Layer Regime    7.1.3  Shallow Layer         7.1.4  Stability of Flow    7.1.5  Conjugate Convection       7.1.6  Non-Newtonian Fluid7.1.7 Other situations     7.2  Side Walls with Uniform Flux or Other Thermal Conditions    7.3  Other Configurations and Effects of Property Variation         7.3.1  Internal Partitions                7.3.2  Effects of Heterogeneity and Anisotropy  7.3.3  Cylindrical or Annular Enclosure     7.3.4  Spherical Enclosure             7.3.5  Porous Medium Saturated with Water Near 4˚C    7.3.6  Attic-Shaped Enclosure     7.3.7  Other Enclosures  7.3.8  Internal Heating7.4  Penetrative Convection        7.4.1  Lateral Penetration             7.4.2  Vertical Penetration            7.4.3  Other Penetrative Flows   7.5  Transient Effects      7.6  Departure from Darcy Flow 7.6.1  Inertial Effects       7.6.2 Boundary Friction, Variable Porosity, Local Thermal Nonequilibrium, Viscous Dissipation, and Thermal Dispersion Effects  7.7  Fluid and Porous Regions     7.8  Sloping Porous Layer or Enclosure    7.9  Inclined Temperature Gradient         7.10 Periodic Heating      7.11 Sources in Confined or Partly Confined Regions        7.12 Effects of Rotation  8 Mixed Convection8.1  External Flow             8.1.1  Inclined or Vertical Plane Wall         8.1.2  Horizontal Wall8.1.3  Cylinder or Sphere               8.1.4  Other Geometries8.1.5  Unified Theory      8.2  Internal Flow:  Horizontal Channel    8.2.1  Horizontal Layer:  Uniform Heating               8.2.2  Horizontal Layer:  Localized Heating             8.2.3  Horizontal Annulus              8.2.4  Horizontal Layer:  Lateral Heating  8.3  Internal Flow:  Vertical Channel         8.3.1  Vertical Layer:  Uniform Heating    8.3.2  Vertical Layer:  Localized Heating   8.3.3  Vertical Annulus:  Uniform Heating              8.3.4  Vertical Annulus:  Localized Heating8.4 Other Geometries and Other Effecrs8.4.1 Partly Porous Configurations8.4.2 Jet Impingement8.4.3 Other aspects 9  Double-Diffusive Convection9.1  Vertical Heat and Mass Transfer        9.1.1  Horton-Rogers-Lapwood Problem                9.1.2  Nonlinear Initial Profiles    9.1.3  Finite-Amplitude Effects   9.1.4  Soret and Dufour Cross-Diffusion Effects9.1.5  Flow at High Rayleigh Number        9.1.6  Other Effects         9.1.6.1  Dispersion           9.1.6.2  Anisotropy and Heterogeneity   9.1.6.3  Brinkman Model               9.1.6.4  Additional Effects             9.2  Horizontal Heat and Mass Transfer  9.2.1  Boundary Layer Flow and External Natural Convection       9.2.2  Enclosed Porous Medium 9.2.3  Transient Effects  9.2.4  Stability of Flow    9.3  Concentrated Heat and Mass Sources            9.3.1  Point Source           9.3.2  Horizontal Line Source       9.4  Other Configurations             9.5  Inclined and Crossed Gradients9.6  Mixed Double-Diffusive Convection9.6.1 Mixed  External Convection9.6.2 Mixed Internal Convection9.7  Nanofluids 10  Convection with Change of Phase10.1  Melting      10.1.1  Enclosure Heated from the Side  10.1.2  Scale Analysis      10.1.3  Effect of Liquid Superheating     10.1.4  Horizontal Liquid Layer    10.1.5 Vertical Melting Front in an Infinite Porous  Medium         10.1.6  A More General Model   10.1.7  Further Studies   10.2  Freezing and Solidification 10.2.1  Cooling from the Side      10.2.1.1  Steady State     10.2.1.2  Other Studies  10.2.2  Cooling from Above          10.2.3  Solidification of Binary Alloys10.3  Boiling and Evaporation      10.3.1  Boiling Produced by Heating from Below 10.3.2  Film Boiling10.3.2  Forced Convection with Evaporation         10.4  Condensation         10.5 Spaces Filled with Fluid and Fibers Coated with a Phase-Change Material 11  Geophysical Aspects11.1  Snow11.2  Patterned Ground                11.3  Thawing Subsea Permafrost             11.4  Magma Production and Magma Chambers                11.5  Diagenetic Processes           11.6  Oceanic Crust          11.6.1  Heat Flux Distribution      11.6.2  Topographical Forcing      11.7  Geothermal Reservoirs:  Injection and Withdrawal                11.8  Other Aspects of Single-Phase Flow              11.9  Two-Phase Flow    11.9.1  Vapor-Liquid Counterflow             11.9.2  Heat Pipes11.9.3  Other Aspects11.10  Cracks in Shrinking Solids11.11 Carbon Dioxide Sequestration11.12 Reaction Scenarios11.12.1 Reaction Fronts11.12 .2 Gradient Reactions11.12.3 Mixing Zones ReferencesIndex